IMPACT OF THE LOCATION PARAMETER ON GAMMA DISTRIBUTION PERFORMANCE IN HYDROLOGICAL APPLICATIONS USING SYNTHETIC SERIES

Código

V-END_II-EBHE0226

Autores

Maria Luíza Teófilo Gandini, PAULO IVO BRAGA DE QUEIROZ

Tema

14 - Eventos e sistemas meteorológicos extremos;

Resumo

This study evaluates the influence of the location parameter (?) on the performance of the three-parameter Gamma distribution (Gamma 3P) compared with the traditional two-parameter Gamma distribution (Gamma 2P) in hydrological applications. Synthetic datasets were generated for sample sizes of 25, 50, and 100 observations under four skewness classes (low, moderate, high, and very high). Two experimental scenarios were considered: datasets generated from Gamma 2P and Gamma 3P. Parameters were estimated using the method of moments, and model performance was assessed through the Kolmogorov-Smirnov (KS) goodness-of-fit test and relative errors of quantiles associated with return periods of 2, 50, and 100 years. The methodology was also applied to four observed annual maximum series (two precipitation and two streamflow datasets). Results showed that, when the true distribution was Gamma 2P, the inclusion of the location parameter provided no systematic improvement in either goodness-of-fit or quantile estimation. Conversely, when the underlying distribution was Gamma 3P, the estimation of ? became more reliable with increasing sample size and skewness, leading to more accurate estimates of long return-period quantiles, particularly for highly skewed datasets. Differences between the two models were substantially more pronounced in quantile estimation than in KS statistics, demonstrating that goodness-of-fit alone is insufficient for selecting probability models intended for hydrological design. The observed datasets confirmed the patterns identified in the synthetic experiments. The results indicate that the practical benefits of the location parameter are restricted to highly skewed datasets, whereas Gamma 2P and Gamma 3P perform similarly in most other situations.